Statistical Analysis on Random Quantum Sampling by Sycamore and Zuchongzhi Quantum Processors

TL;DR

This paper compares the statistical properties of outputs from random quantum sampling on Sycamore and Zuchongzhi quantum processors, revealing differences in their closeness to classical randomness and raising questions about reliability.

Contribution

It provides a comparative statistical analysis of two quantum processors' outputs, highlighting differences and stability in their sampling properties.

Findings

Zuchongzhi's samples are closer to classical uniform randomness than Sycamore's.

Some Zuchongzhi bit-strings pass randomness tests, unlike Sycamore.

Statistical properties remain stable as circuit depth increases.

Abstract

Random quantum sampling, a task to sample bit-strings from a random quantum circuit, is considered one of suitable benchmark tasks to demonstrate the outperformance of quantum computers even with noisy qubits. Recently, random quantum sampling was performed on the Sycamore quantum processor with 53 qubits [Nature 574, 505 (2019)] and on the Zuchongzhi quantum processor with 56 qubits [Phys. Rev. Lett. 127, 180501 (2021)]. Here, we analyze and compare statistical properties of the outputs of random quantum sampling by Sycamore and Zuchongzhi. Using the Marchenko-Pastur law and the Wasssertein distances, we find that quantum random sampling of Zuchongzhi is more closer to classical uniform random sampling than those of Sycamore. Some Zuchongzhi's bit-strings pass the random number tests while both Sycamore and Zuchongzhi show similar patterns in heatmaps of bit-strings. It is shown that statistical properties of both random quantum samples change little as the depth of random quantum circuits increases. Our findings raise a question about computational reliability of noisy quantum processors that could produce statistically different outputs for the same random quantum sampling task.